Solving One-Step Solving One-Step InequalitiesInequalities
763 542 8
127 >+x 127 >+x
Objective: To solve one-step inequalities using
properties for inequalities
Solving One-Step Solving One-Step InequalitiesInequalities
Solving One-Step Solving One-Step InequalitiesInequalities
What are the Properties for Inequalities?
Are they the same as for regular equations?
Solving One-Step InequalitiesSolving One-Step Inequalities
Addition Property for Inequalities
X-15<73 X-
15+15<73+15X<88
Add 15 to both sides
Solving One-Step InequalitiesSolving One-Step Inequalities
Subtraction Property for Inequalities
y+15<25 Y+15-15<25-
15 y<10
Subtract 15 from both sides
Solving One-Step InequalitiesSolving One-Step Inequalities
Multiplication Property for Inequalities
105
=x
5105
5 ×=×x
50=xMultiply both sides by the reciprocal of the coefficient
Solving One-Step InequalitiesSolving One-Step Inequalities
Division Property for Inequalities
205 >x
5
20
5
5>
x
4>x
Divide both sides by the coefficient of x
Division Property for Inequalities Caution! Dividing
by a negative number205 <− x
5
20
5
5
−<
−− x
4−>x
Notice: Sign CHANGED
Same if multiplying?
Multiplication Property for Inequalities
Caution! When you multiply by a negative number…
…the sign CHANGES
YES!-x > 2
5
(-5 )-x > 2(-5) 1 5
x < -10
Solving One-Step Solving One-Step InequalitiesInequalities
Let’s try some on our own …… ready?
Solving One-Step Solving One-Step InequalitiesInequalities
76 ≤+x 1
Solving One-Step Solving One-Step InequalitiesInequalities
53 −≤x 2
Solving One-Step Solving One-Step InequalitiesInequalities
153 −≥− x 3
Solving One-Step Solving One-Step InequalitiesInequalities
59 −>−x 4
1.1.x ≤ x ≤ 112.2. 8 ≤ x or x ≥ 88 ≤ x or x ≥ 8
3.3. x ≤ 5x ≤ 5
4.4. x > 4x > 4
Answers for #1 - #4Answers for #1 - #4
Solving One-Step Solving One-Step InequalitiesInequalities
32
1−≥x
5
Solving One-Step Solving One-Step InequalitiesInequalities
73
−>−
x 6
Solving One-Step Solving One-Step InequalitiesInequalities
75 ≥+ x 7
Solving One-Step Solving One-Step InequalitiesInequalities
53
>x 8
Answers for #5 - #8Answers for #5 - #8
5.5. x ≥ -6 x ≥ -6
6.6. 21 < x or x > 21 21 < x or x > 21
7.7. x ≥ 2 x ≥ 2
8. 8. x > 15x > 15
Please take out a Please take out a piece of paper and piece of paper and write down what the write down what the steps are for solving steps are for solving a one-step inequalitya one-step inequality
Reflection
Solving One-Step Inequalities
Excellent Job !!! Well Done